We design a novel algorithm for optimal transport by drawing from the entropic optimal transport, mirror descent and conjugate gradients literatures. Our algorithm is able to compute optimal transport costs with arbitrary accuracy without running into numerical stability issues. The algorithm is implemented efficiently on GPUs and is shown empirically to converge more quickly than traditional algorithms such as Sinkhorn's Algorithm both in terms of number of iterations and wall-clock time in many cases. We pay particular attention to the entropy of marginal distributions and show that high entropy marginals make for harder optimal transport problems, for which our algorithm is a good fit. We provide a careful ablation analysis with respect to algorithm and problem parameters, and present benchmarking over the MNIST dataset. The results suggest that our algorithm can be a useful addition to the practitioner's optimal transport toolkit. Our code is open-sourced at https://github.com/adaptive-agents-lab/MDOT-PNCG .

翻译：我们通过融合熵正则化最优传输、镜像下降和共轭梯度三类文献，设计了一种新型最优传输算法。该算法能够在避免数值稳定性问题的前提下，以任意精度计算最优传输成本。算法在GPU上高效实现，实验表明，在迭代次数和实际运行时间两方面，其收敛速度通常优于Sinkhorn算法等传统方法。我们特别关注边际分布的熵，并证明高熵边际分布会导致最优传输问题更难求解，而我们的算法恰好适用于此类场景。我们对算法参数和问题参数进行了细致的消融分析，并在MNIST数据集上进行了基准测试。结果表明，该算法可成为实践者最优传输工具包中的有益补充。我们的代码已开源在https://github.com/adaptive-agents-lab/MDOT-PNCG。